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I'm trying to understand this classical Sequent Calculus proof.

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These are the rules Of Sequent Calculus(version 1) in respect to this question enter image description here enter image description here

How do we know to use [v R2] and [v R1] instead of [v L] which I originally used

and also on why we know to use [v R2] on A⊢(A→B) ∨ (B→A) and [v R1] on ¬A⊢(A→B) ∨ (B→A) and not the other way around.

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    The rule $\lor L$ needs the same formula (called $C$ in the rule) on the right side of $\vdash$ in both premises. At the stages where the proof used $\lor R_1$ and $\lor R_2$, the right sides of the premises were different ($B\to A$ and $A\to B$), so $\lor L$ couldn't be applied. – Andreas Blass Jul 28 '22 at 17:09
  • @AndreasBlass thankyou, but now how do we know whether to use ∨R1 or ∨R2 –  Jul 28 '22 at 17:15
  • Which $\lor R$ rule to use is determined by the fact that you want the final conclusion to be $(A\to B)\lor(B\to A)$ rather than $(B\to A)\lor(A\to B)$. – Andreas Blass Jul 28 '22 at 17:19

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